Monthly Archives: June 2016

The ingenious pieces of Sei Shonagon

Tangram is one of the best known puzzles in the world, and went through at least two fads: one in the early nineteenth century, and once more when American puzzlist Sam Loydd published a booklet about it. The oldest known tangram dates back to about 1800.

In 1742, a little book about a Japanese seven-piece puzzle was published under the pseudonym Ganreiken. The real name of the author is unknown. The title was “Sei Shonagon Chie-no-ita”, or the ingenious pieces of Sei Shonagon. Sei Shonagon was a court lady who lived approximately 966 – 1017. There is no clear reason why Ganreiken named his 32 page booklet after her. The booklet has 42 patterns with answers, but the shapes are inaccurate. A copy of the booklet has been distributed at one of the International Puzzle Parties, but as I’m not in contact with anyone in higher puzzle circles I don’t have access to it. A year later Ganreiken published another book with more exercises. In about 1780, Takahiro Nakada wrote a manuscript entitled “Narabemono 110 (110 Patterns of an Arrangement Pattern),” and Edo Chie-kata (Ingenious Patterns in Edo) was published in 1837. Alas I was unable to find these figures on the internet.

There are surprisingly few publications in the west about this puzzle. Jerry Slocum devotes half a page of it in his book “The history of Chinese Tangram”, and Jerry Slocumn and Jack Botermans describe it in their “Zelf puzzels maken en oplossen”.

The Sei Shonagon consists of 7 pieces, like Chinese Tangram, which make up a square. Unlike Tangram, they can be fitted together to make up a square in two different ways.
sei shonagon square 1

I will leave the other square as an exercise for you.

They can also form a square with a whole in the middle:
sei shonagon square with hole in centre

The figure with the hole in the middle is one of the original puzzles.

Where the Chinese tangram has 13 convex shapes, Philip Moutou showed that Chie no-ita has 16 possible convex shapes. In geometry, a shape is called convex if any two points of the figure can be connected by a straight line which is entirely within the figure. I intend to publish about them in a subsequent post.

Presented here are 28 of the original problems.

japanese tangram blogpost 1-1 exercises

japanese tangram blogpost 1-2 exercises

japanese tangram blogpost 1-3 exercises

japanese tangram blogpost 1-4 exercises

japanese tangram blogpost 1-5 exercises

japanese tangram blogpost 1-6 exercises

japanese tangram blogpost 1-7 exercise

You can check your solutions here

A new puzzle is published every Friday. Solutions are published after one or more weeks. You are welcome to discuss the puzzles, their difficulty level, originality and much more.

The hiker, the bicycle and the moped

Hiker, cyclist and moped

Alexandra, Bernadette and Cindy all want to go from A to B. The distance is 60 km. (If you prefer miles, simply read miles instead of kilometers in this puzzle.)

They have a bicycle and a moped. Both are without backseat, so only one person can use them at any time.
A hiker walks 5 km/hour.
A Cyclist goes 10 km/hour.
The moped rider makes 20 km/hour.

A hiker would take 60/5=12 hours.
A cyclist would take 60/10=6 hours
The moped rider would take 60/20= 3 hours.
Together that is 12+6+3=21 hours, or 7 hours average.

Is there a way, by alternating transport means, that the three people all can make it in 7 hours?

If you are stuck, one possible solutions is given here. Be aware that more solutions are possible.

This puzzle is based on a similar problem in Pythagoras, issue 1 1967/1968. The distance and the speeds have been changed.

It is easy to see simplify this problem to 2 persons, A and B. The solutions become pretty trivial. But how about expanding the puzzle to 4 people, or 5, or even to n people?

A new puzzle is published every friday. You are welcome to comment on the puzzles. Solutions are usually added after one or more weeks.


In the picture below you find 6 matchsticks. If we assume a matchstick is 1 inch long, the enclosed surfce has a size of 2.

triangle surfaces 2016-01-26 exercise as square

Now rearrange the 6 matches into two figures of 6 matchsticks each, in such a way that the surface of one figure is exactly 1.5 time the surface of the other figure.

You can check your solutions here

A new puzzle is published every Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to three stars.

Bongard problem (7)

The Russian scientist M.M. Bongard published a book in 1967 that contains 100 problems. Each problem consists of 12 small boxes: six boxes on the left and six on the right. Each of the six boxes on the left conform to a certain rule. Each and every box on the right contradicts this rule. Your task, of course, is to figure out the rule.

Bongard problem 7 rule 10 exercise

You can check your solutions here

You can find more Bongard problems at Harry Foundalis site, and I intend to publish more problems in the future.

A new puzzle is posted every friday. You are welcome to comment on the puzzles. Solutions are added at the bottom of a puzzle after one or more weeks.